[1]} addressed a similar problem using backward recursion. Their motivating problem was a recurrent disease clinical trial where patients receive an initial treatment followed by a salvage treatment if patients experience either treatment resistance or relapse.
[2]} extended the dynamic treatment regime estimator for continuous outcomes via weighted least squares [3]} into the censored time-to-event data setting. Both of these methods use the accelerated failure time model for the failure time distribution, which carries a risk of model misspecification. Thus, a more flexible model is needed to allow for more relaxed distributional assumptions.
[4]} proposed a dynamic treatment regime estimator using full specification of the likelihood and [5]} developed a Bayesian alternative, where the disease progression dynamic was modeled using a dependent Dirichlet process prior with Gaussian process measure. While the latter approach provides a more flexible modeling framework than the former, the class of regimes for both methods is refined to a fixed number of pre-defined treatment sequences.
